Folding Amplitudes into Form Factors: An Antipodal Duality

Area of Science:

• High-energy physics
• Quantum field theory
• String theory

Background:

• Planar N=4 super-Yang-Mills theory is a key model in quantum field theory.
• The stress-tensor multiplet and gluon amplitudes are fundamental quantities in this theory.
• Hopf algebra structures and polylogarithms are advanced mathematical tools used in theoretical physics.

Purpose of the Study:

• To investigate the duality between the three-gluon form factor and the six-gluon MHV amplitude.
• To identify the mathematical map governing this observed duality.
• To provide computational evidence for the duality up to higher loop orders.

Main Methods:

• Calculation of the three-gluon form factor for the chiral part of the stress-tensor multiplet.
• Analysis of the six-gluon MHV amplitude on its parity-preserving surface.
• Application of the antipode operation from polylogarithm Hopf algebra structure.
• Symbolic computation and verification up to seven loops.

Main Results:

• A precise duality is established between the three-gluon form factor and the six-gluon MHV amplitude.
• The duality is mathematically characterized by the antipode operation on polylogarithms.
• The relationship holds and is verified through extensive loop calculations.

Conclusions:

• The observed duality provides a novel connection between different observables in N=4 super-Yang-Mills theory.
• The antipode operation offers a powerful tool for understanding these relationships.
• This finding deepens our understanding of the mathematical structures underlying quantum field theories.